Origin of difference between<i>u</i>¯ and<i>d</i>¯ partons in the nucleon

Abstract

Using the Euclidean path-integral formulation for the hadronic tensor, we show that the large difference between u\ifmmode\bar\else\textasciimacron\fi{} and d\ifmmode\bar\else\textasciimacron\fi{} does not come from the disconnected quark-loop insertion. Rather, it can come from the connected (quark line) insertion involving quarks propagating backwards in time. We study the influence of the backward time propagator in the axial-vector and scalar matrix elements in lattice gauge calculations and give an estimate of the violation of the Gottfried sum rule.